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BITSAT 2013

Exam: BITSAT
Year: 2013
Subject: Mathematics
Chapter: Binomial Theorem

BITSAT 2013 · Mathematics · Binomial Theorem

The coefficient of the middle term in the expansion of (2+3 x)^ 4...

The coefficient of the middle term in the expansion of

(2+3 \mathrm{x})^{4}

is:

Options

A6
B $5 !$
C $8 !$
D216

Correct answer

D. 216

Step-by-step solution

When exponent is

n

then total number of terms are

\mathrm{n}+1.

So, total number of terms in

(2+3 x)^{4}=5

Middle term is 3rd.

\Rightarrow \mathrm{T}_{3}={ }^{4} \mathrm{C}_{2}(2)^{2} \cdot(3 \mathrm{x})^{2}=\frac{4 \times 3 \times 2 \times 1}{2 \times 1 \times 2} \times4 \times9 \mathrmx^{2}=216 \mathrmx^{2}

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